Name:____________________________________________

Teaneck Public Schools Summer Assignment
Algebra II and Algebra II Trig Honors

Below are the directions and policies for the summer packet

	This is a summer packet for students entering into Algebra II/H Algebra II with Trig course. This packet is due on the first day of school.

	The summer assignment is due the first day of class. On the first day of class, teachers will collect summer assignments. Any student who does not have the assignment will be given one by the teacher. Late projects will lose 10 points each day.

	This summer assignment will be graded on completion. Completion is defined as having all work shown in the space provided to receive full credit, and a parent/guardian signature. A preliminary assessment (administered during the first week of school) will be based on the topics covered in this packet.

	Any student who registers as a new attendee of Teaneck High School after August 15th will have an extra week to complete the summer assignment.

	Summer assignment packets will be available on the district web site and available in the THS guidance office.

The list below contains topics covered in Algebra I that students are expected to know upon entering Algebra II. Each section contains 3 steps: Step 1 allows students to review the mathematical concept with Khan Academy and/or Desmos, Step 2 shows how the concepts are used in problems with detailed solutions, and Step 3 provide opportunities for students to try the problems on their own.

Check (✓) as you complete each section:

Part 1: Solving Systems of Linear Equations

______1.1. Solving Systems of Linear Equation by Graphing

______1.2. Solving Systems of Linear Equations by Substitution

______1.3. Solving Systems of Linear Equations by Elimination

______1.4. NJSLA Questions

Part 2: Solving Quadratic Equation

______2.1. Solving Quadratic Equations by Graphing

______2.2. Solving Quadratic Equations by Using Square Roots

______2.3. Solving Quadratic Equations by Completing the Square

______2.4. Solving Quadratic Equations by Using the Quadratic Formula

Part 3: Putting it all together…

______3.1. Solving Nonlinear Systems of Equations

______3.2. NJSLA Questions

Part 1: Solving Systems of Linear Equations

1.1. Solving Systems of Linear Equation by Graphing

Step 1: Watch this video: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-graphically/v/solving-linear-systems-by-graphing

Then, go to student.desmos.com and type in QNJUWZ and complete the task.

Step 2: Review the solved examples

Example 1) Solve the system of linear equations by graphing:

𝑦 = −𝑥 + 5	𝑦 = 2𝑥 − 1

Example 2) Solve the system of linear equations by graphing:

2𝑥 + 𝑦 = 5	3𝑥 − 2𝑦 = 4

Step 3: Solve the system of equations by graphing.

1. 3x  5y  2 y  2

3
3.	y  2 x  3

1
y  2 x  5

2. x  4y  10 2x  3y  5

4. 3x  3y  3

5x  2y  1

5. For each rectangle below, write a linear equation that represents the area y of the rectangle. Solve this system of two linear equations by graphing. Interpret your solution.

1.2. Solving Systems of Linear Equations by Substitution

Step 1: Watch the video: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-with-substitution/v/the-substitution-method

Step 2: Review the solved examples

Example 1) Solve the following equations by substitution

Example 2) Solve the system of equations by substitution

2𝑥 − 𝑦 = 2	2𝑥 + 𝑦 = 6

Step 3: Solve the systems of equations by substitution.

1.
2x  2y  4
y  12  3x
	2.
5x  5y  10
3x  7y  4
	3.
x  y  4
2x  3y  3

4. Write an equation that represents the sum of the angle measures of the parallelogram and use your equations and the equation shown to find the values of x and y.

1.3. Solving Systems of Linear Equations by Elimination

Step 1. Watch the video: https://www.khanacademy.org/math/algebra-home/alg-system-of-equations/alg-equivalent-systems-of-equations/v/solving-systems-of-equations-by-elimination

Step 2. Review the solved examples.

Step 3. Solve the systems of equations by elimination.

4x  y  5 1.	3x  y  9
	2x  7y  5 2.	x  y  10
	
10x  3y  30 3.	15x  8y  45
	7x  6y  9 4.	5x  2y  19

5. You are ordering T-shirts for Teaneck HS. The table shows the order for 45 students.

a. How many students ordered medium and large shirts?

Small
	Medium
	Large
	
11
	x
	y

b. The number of students who ordered a medium T-shirt was two less than the number of students who ordered a large T-shirt. Write a system of linear equations that represents the number of students who ordered medium and large T-shirts.

c. Solve the system of linear equations by elimination.

d. You are ordering 10 additional medium and large T-shirts for new members who might join the school. Based on your answers in part c, how many of each size would you order? Explain.

1.4. NJSLA Questions

Make sure to show all work!

Answer:

Answer:

Part 2: Solving Quadratic Equation

2.1. Solving Quadratic Equations by Graphing

Step 1. Watch the video: https://www.khanacademy.org/math/algebra2/advanced-functions/systems-of-quadratic-equations/v/non-linear-systems-of-equations-1

Then, go to student.desmos.com and type in XN6X5A and complete the task.

Step 2. Review the solved examples.

Step 3. Solve the quadratic equations by graphing. Feel free to utilize Desmos calculator!

1. x2  3x  6  0
	2. 8x  15  x2
	
3. 9  x2  8x
	4. x2  2x  3

5. The height h (in feet) of a ball in a baseball game can be modeled by h  16t2  28t  8, where t is the time (in seconds).

a. Do both t-intercepts of the graph of the function have meaning in this situation? Explain.

b. No one caught the ball. After how many seconds did the ball hit the ground?

2.2. Solving Quadratic Equations Using Square Roots

Step 1. Watch the video: https://www.khanacademy.org/math/algebra/quadratics/quadratics-square-root/v/simple-quadratic-equation

Step 2. Review the solved examples.

Step 3. Solve the equations using square roots.

1. x2  8  10
	2. x2  25  25
	
3. x  22  9
	4. 2x2  10  0

Determine the number of real solutions of the equation. Then, solve the equation using square roots.

5. x2  36	6. x2  16	7. x2  0


8. A can of juice has a height of 10 inches and a volume of 160 cubicinches. The volume of a can with radius r is given by the formula V  r2h.

a. Write an equation describing this situation, where r is the radius of the can.

b. Find the radius of the can.

2.3. Solving Quadratic Equations by Completing the Square

Step 1. Watch the video: https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-by-completing-the-square/v/solving-quadratic-equations-by-completing-the-square

Step 2. Review the solved examples: https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-by-completing-the-square/e/completing_the_square_in_quadratic_expressions

Step 3. Solve the equations by completing the square.

1. x2  6x  18  0
	2. x2  2x  15  0
	
3.	4x2  16x  19  17
	4.	2x2  16x  20  0
	
5.	x2  3x  7
	6.	x2  15x  12

7. The product of two consecutive odd integers that are positive is 323.

a. Write an equation to find the integers.

b. Find the two integers.

2.4. Solving Quadratic Equations by Using the Quadratic Formula

Step 1. Watch the video: https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadratic-formula/v/quadratic-formula-1

Step 2. Review the solved examples

Example:	Checking solutions:

Step 3. Solve the equations by using the quadratic formula.

1. x2  5x  14  0
	2. 3x2  2x  1  0
	
3. 5x2  9x  3
	4. 3x2  2x  6
	
5.	7x2  21x
	6.	5x2  4x  10

7. Consider the equation 3x2  5x  6  0.

a. Use the discriminant to determine the number of solutions. (Discriminant review: https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadratic-formula/a/discriminant-review)

b. Change the sign of c in the equation. Write the new equation:________________________________________

c. Use the discriminant to determine the number of solutions of the new equation. Did your answer change? Explain.

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

Part 3: Solving Systems of Linear and Quadratic Equations

3.1. Solving Systems of Nonlinear Equations

Step 1: Watch this video: https://www.khanacademy.org/math/algebra2/advanced-functions/systems-of-quadratic-equations/v/non-linear-systems-of-equations-1

Step 2: Review the solved examples

2
Step 3.

#1-2. Solve each system by graphing.
	
1.	y  2x2  3x  1 y  x  1
	2.	y  1x2  2x  3

y  x  1

#3-6. Solve each system by substitution.
	
3.	y  x  4
y  x2  3x  4
	4.	y  x2  3 y  3x  7
	
5.	y  6x
y  x2  9
	6.	y  3  x2 y  3

#7-10. Solve each system by elimination.
	
7.	y  4x2  8x  8 y  8x  4
	8.	y  2x2  x  6 y  x  2
	
9.	y  2x2  2x y  2x  6
	10.	y  x2  4x  7 y  x  11

11. The graphs of f x  1.6x2  2x  0.6 and gx  2.5x2  2x  4.2 do not intersect. Change the value(s) of c in one or both functions of f and g until the two graphs do intersect. Write your new system of equations and determine the intersection point(s), rounding to the nearest hundredth, if necessary.

3.2. NJSLA Questions

Make sure to show all work!